Table 1.

Comparison of single versus composite run Bayes Factor estimation.

Annealing Integration
δβ = 0.001	Integration interval	Q.E.	σd	σs	total error
Q = 200	0.00 – 0.10	-121.7	11.7	2.0	14.9
	0.10 – 0.20	57.3	0.1	0.4	0.7
	0.20 – 0.30	68.9	0.0	0.2	0.4
	0.30 – 0.40	74.3	0.0	0.2	0.3
	0.40 – 0.50	77.8	0.0	0.2	0.3
	0.50 – 0.60	80.6	0.0	0.1	0.2
	0.60 – 0.70	82.1	0.0	0.1	0.2
	0.70 – 0.80	83.9	0.0	0.1	0.2
	0.80 – 0.90	87.0	0.0	0.2	0.3
	0.90 – 1.00	102.7	1.3	1.5	3.8
Total	0.00 – 1.00	592.9	13.2	4.9	21.3
Composite Run log Bayes Factor: 592.9
Composite Run Confidence Interval: [571.6; 614.2]
Single Run log Bayes Factor: 592.7. σd = 13.4. σs = 2.5. σ = 17.6
Single Run Confidence Interval: [575.1; 610.2]
Melting Integration
δβ = 0.001	Integration interval	Q.E.	σd	σs	total error
Q = 200	1.00 – 0.90	121.7	8.2	3.3	13.7
	0.90 – 0.80	87.5	0.0	0.2	0.3
	0.80 – 0.70	84.5	0.0	0.1	0.2
	0.70 – 0.60	82.7	0.0	0.1	0.2
	0.60 – 0.50	80.8	0.0	0.1	0.2
	0.50 – 0.40	77.9	0.0	0.2	0.3
	0.40 – 0.30	74.5	0.0	0.2	0.3
	0.30 – 0.20	69.1	0.0	0.2	0.4
	0.20 – 0.10	58.1	0.1	0.4	0.7
	0.10 – 0.00	-42.9	3.2	1.4	5.6
Total	1.00 – 0.00	693.8	11.7	6.2	21.9
Composite Run log Bayes Factor: 693.8
Composite Run Confidence Interval: [671.9; 715.7]
Single Run log Bayes Factor: 693.6. σd = 12.3. σs = 3.6. σ = 18.3
Single Run Confidence Interval: [675.3; 711.9]

Comparison of single versus composite run Bayes Factor estimation reveals virtually identical log Bayes Factors, but tighter confidence intervals for the single run calculation, both in the annealing and melting scheme of the thermodynamic integration approach. A constant increment δβ (or decrement) of 0.001 was used for β with Q = 200 iterations for each value of β. Q.E. is the quasistatic estimator for each (thermodynamic) integration interval with discrete and sampling error denoted by σ_d and σ_s, respectively.